Mobile computing devices, such as mobile phones and computer tablets, continue to employ designs focused on decreasing size requirements. The trend toward miniaturization of mobile computing devices requires the use of smaller internal components. Tunable filters are one such internal component that affect the overall size of a mobile computing device. One way to construct a tunable filter is through the use of transmission lines. Notably, tunable filters require slower wave signals, and thus, transmission lines used to construct tunable filters should be designed to transmit wave signals at compatible speeds. Three factors that affect the speed at which transmission lines transmit wave signals are size, permittivity (∈), and permeability (μ).
FIG. 1 illustrates an exemplary transmission line 10 disposed along a ground plane 12. The transmission line 10 is separated from the ground plane 12 by a distance (D), wherein, as a non-limiting example, the distance (D) may include a dielectric layer (not shown). Further, the transmission line 10 is employed using a low cost, low permittivity (∈low) material. The speed at which a wave signal is transmitted (the velocity factor (Vf) (not shown)) by the transmission line 10 is inversely proportional to the square root of the relative permittivity (Vf=1/√∈(r)). Thus, the ∈low material causes the transmission line 10 to have a higher Vf as compared to transmission lines constructed using a higher permittivity material. To delay a transmitted wave signal in light of the higher Vf, the transmission line 10 is designed with a longer length (Llong) so as to require a transmitted wave signal to travel a further distance. Additionally, the transmission line 10 is designed with a wider width (Wwide) to reduce loss. Therefore, to transmit a wave signal at a speed that is compatible with a tunable filter while achieving low loss, the transmission line 10 requires a larger area to overcome the higher Vf associated with the ∈low material. However, the larger area of the transmission line 10 may not be desirable for tunable filters implemented in mobile computing devices with limited area requirements.
To transmit a wave signal at a speed that is compatible with a tunable filter while requiring less area than the transmission line 10, a transmission line may be constructed using a high permittivity ∈high material. In this manner, FIG. 2 illustrates an exemplary transmission line 14 employed using a high cost, ∈high material disposed along a ground plane 16. Notably, the transmission line 14 is separated from the ground plane 16 by a distance (D). The ∈high material causes the transmission line 14 to have a lower Vf as compared to transmission lines constructed using a ∈low material, such as the transmission line 10. Because the transmission line 14 has a lower Vf, a transmitted wave signal does not need to be delayed by employing a longer length (Llong), allowing the transmission line 14 to be designed with a shorter length (Lshort). However, the transmission line 14 is also designed with narrower width (Wnarrow), which causes increased loss. Thus, although the transmission line 14 consumes less area than the transmission line 10, the transmission line 14 incurs greater loss and requires a higher cost material.
Therefore, it would be advantageous to employ a transmission line designed to transmit wave signals at speeds compatible with tunable filters while achieving reduced area, costs, and loss.